Voltage regulation in wireless power receivers

ABSTRACT

A wireless power receiver includes one or more tunable capacitors in parallel with an inductor. The wireless power receiver adapted to receive an induced voltage input at the inductor due to a magnetic field generated by a wireless power transmitter. The rectifier has an output with a rectified voltage and a rectified current. A controller has a first input for receiving a signal representative of the rectified voltage and a first output for supplying an adjustment signal to the tunable capacitor. The controller includes a processor coupled to the first input and is configured to operate on the signal representative of rectified voltage to produce a desired capacitance value for capacitor and provide the adjustment signal determined so as to adjust a capacitance value of capacitor to the desired capacitance value.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a continuation of U.S. patent applicationSer. No. 15/602,775 filed on May 23, 2017 and entitled “VOLTAGEREGULATION IN WIRELESS POWER RECEIVERS”, which claims priority to U.S.Provisional Patent Application No. 62/342,525, filed May 27, 2016,entitled, “VOLTAGE REGULATION IN WIRELESS POWER RECEIVERS”, thedisclosures of which are incorporated herein, in their entirety, byreference.

TECHNICAL FIELD

The disclosure generally relates to wireless power systems and, moreparticularly, the disclosure relates to voltage regulation in wirelesspower receivers in wireless power systems.

BACKGROUND

Wireless power receivers can receive power from wireless powertransmitters via an oscillating magnetic field generated by thetransmitter. Wireless power receivers can be coupled to electronicdevices of varying power requirements. The power requirements ofelectronic devices, such as smartphones and laptops, can vary as theassociated battery or batteries charge or discharge.

SUMMARY

In accordance with one embodiment, a wireless power receiver includes acircuit comprising a tunable capacitor C₂ in parallel with an inductorL₁, the wireless power receiver adapted to receive an induced voltageinput V_(induced) at the inductor L₁ due to a magnetic field generatedby a wireless power transmitter, the wireless power receiver having aneffective series resistance R_(receiver). The receiver further includesa rectifier coupled to the circuit, the rectifier having an output witha rectified voltage V_(rect) and a rectified current I_(rect), and acontroller having a first input for receiving a signal representative ofthe rectified voltage V_(rect) and a first output for supplying anadjustment signal to the tunable capacitor C₂. The controller caninclude a processor coupled to the first input and be configured to (i)operate on the signal representative of rectified voltage V_(rect) toproduce a desired capacitance value C_(2_desired) for capacitor C₂ and(ii) provide the adjustment signal determined so as to adjust acapacitance value C_(2_value) of capacitor C₂ to the desired capacitancevalue C_(2_desired).

In a related embodiment, the processor is configured to compare thesignal representative of rectified voltage V_(rect) to a range ofvoltages defined by an upper limit V_(upper) and a lower limitV_(lower), the range of voltages stored in a memory of the controller;and the controller can be configured to transmit the adjustment signalto the tunable capacitor C₂ in response to the comparison of the valueof rectified voltage V_(rect) to the range of voltages.

In another related embodiment, the controller, to produce the desiredcapacitance value C_(2_desired), is configured to (iv) receive, at asecond input of the controller, a signal representative of a rectifiedcurrent L_(ea) of the rectifier output, (v) operate, in the processor,on the signals representative of each of the rectified voltage V_(rect)and current I_(rect) to determine power P_(L) to a load coupled to therectifier output and resistance R_(L) at the load, (vi) operate, in theprocessor, on the receiver resistance R_(receiver) and power P_(L) todetermine power P_(receiver) to the receiver, and (vii) operate, in theprocessor, on power P_(receiver), a value of capacitor C₂, and a valueof capacitor C₃ to determine an open circuit voltage value V_(open),wherein the desired capacitance value C_(2_desired) is a function ofV_(open).

Optionally, a wireless power receiver further includes a tunablecapacitor C₃ coupled in series with the circuit, wherein the controllerincludes a second output for supplying an adjustment signal to thetunable capacitor C₃. In some embodiments, the memory of the controllerincludes a lookup table that includes capacitance values C_(3_value) forgiven capacitance values C_(2_value) and load voltage valuesV_(L_value), for at least one load resistance value R_(L_value).

In a related embodiment, the controller selects the capacitance valueC_(3_value) of the tunable capacitor C₃ such that the capacitance valuesC_(2_value) and C_(3_value) are resonant with the inductance L_(1_value)of inductor L₁, with a resonance frequency f_(resonant). Optionally, theresonant frequency f_(resonant) is approximately 6.78 MHz.

In a further related embodiment, capacitor C₃ includes two or morecapacitors coupled in parallel or in series. Optionally, capacitor C₃includes a switched capacitor, pulse width modulation (PWM) controlledcapacitor, varactor, or barium strontium titanate (BST) capacitor.Optionally, a wireless power receiver includes a means for adjusting acapacitance value C_(3_value) of capacitor C₃. In some embodiments, awireless power receiver includes a means for adjusting a capacitancevalue C_(2_value) of capacitor C₂.

In a related embodiment, a wireless power receiver further includes atunable capacitor C₃ coupled in series with the circuit, wherein thecontroller, during the operation, (v) transmits, via a second outputcoupled to the processor, an adjustment signal to the tunable capacitorC₃ to adjust a capacitance value C_(3_value) the capacitor C₃ inresponse to the comparison of the value of rectified voltage V_(rect) toof the range of voltages.

In a further related embodiment, capacitor C₂ comprises two or morecapacitors coupled in parallel or in series. Optionally, a wirelesspower receiver further includes a tunable capacitor C₁ coupled in serieswith the inductor L₁, wherein the controller includes a third output forsupplying an adjustment signal to the tunable capacitor C₁.

In accordance with another embodiment, a method is disclosed herein forregulating rectified voltage V_(rect) in a system including a controllercoupled to a wireless power receiver, the wireless power receiverincluding a rectifier coupled to a circuit, the circuit comprising atunable capacitor C₂ in parallel with an inductor L₁, the wireless powerreceiver having an effective series resistance R_(receiver), therectifier having an output with a rectified voltage V_(rect) and arectified current I_(rect). The method includes (i) receiving, at afirst input of the controller, a signal representative of a rectifiedvoltage V_(rect), (ii) operating, in a processor coupled to the firstinput, on the signal representative of the rectified voltage V_(rect) toproduce a desired capacitance value C_(2_desired) for capacitor C₂, and(iii) providing, via a first output of the controller, an adjustmentsignal so as to adjust a capacitance value C_(2_value) of capacitor C₂to the desired capacitance value C_(2_desired).

In a related embodiment, the method further includes (iv) comparing, bythe processor, the signal representative of the rectified voltageV_(rect) to a range of voltages defined by an upper limit V_(upper) andlower limit V_(lower), the range of voltages stored in a memory of thecontroller, and (v) transmitting, via the first output of thecontroller, the adjustment signal to the tunable capacitor C₂ inresponse to the comparison of the signal representative of the value ofrectified voltage V_(rect) to the range of voltages.

In an alternate embodiment, producing the desired capacitance valueC_(2_desired) further includes (iv) receiving, at a second input of thecontroller, a signal representative of a rectified current I_(rect), (v)operating, in the processor, on the signals representative of each ofthe rectified voltage V_(rect) and current I_(rect) to determine powerP_(L) to a load coupled to the rectifier output and resistance R_(L) atthe load, (vi) operating, in the processor, on the receiver resistanceR_(receiver) and power P_(L) to determine power P_(receiver) to thereceiver, and (vii) operating, in the processor, on power P_(receiver)to determine an open circuit voltage value V_(open), wherein the desiredcapacitance value C_(2_desired) is a function of V_(open).

In yet another related embodiment, the method further includes (viii)transmitting, via a second output coupled to the processor, anadjustment signal to a tunable capacitor C₃ coupled in series with thecircuit. Optionally, the method further includes (ix) selecting, from alookup table stored in a memory of the controller, a capacitance valueC_(3_value) for given capacitance values C_(2_value) and load voltagevalues V_(L) for at least one load resistance R_(L). In some embodiment,the method further includes (x) adjusting, by the processor, thecapacitance value C_(3_value) of the tunable capacitor C₃ such that thecapacitance values C_(2_value) and C_(3_value) are resonant with theinductance L_(1_value) of inductor L₁, with a resonance frequencyf_(resonant).

BRIEF DESCRIPTION OF THE DRAWINGS

Those skilled in the art should more fully appreciate advantages ofvarious embodiments from the following “Detailed Description,” discussedwith reference to the drawings summarized immediately below.

FIGS. 1-2 show diagrams of exemplary embodiments of wireless powersystems.

FIGS. 3A, 3B, and 4 show diagrams of exemplary embodiments of wirelesspower receivers.

FIGS. 5, 6A, and 6B show diagrams of exemplary embodiments of capacitornetworks for wireless power receivers.

FIG. 7 shows a diagram of an exemplary embodiment of a wireless powerreceiver coupled to control and logic circuitry.

FIGS. 8A, 8C, 8E, and 8G show diagrams of exemplary embodiments ofimpedance matching networks for wireless power receivers. FIG. 8B showsa plot of rectified voltage as a function of capacitance C₁ values forthe receiver shown in FIG. 8A.

FIG. 8D shows a plot of rectified voltage as a function of capacitanceC₂ values for the receiver shown in FIG. 8C. FIG. 8F shows a diagram ofan equivalent circuit for the receiver shown in FIG. 8E. FIG. 8H shows adiagram of an equivalent circuit for the receiver shown in FIG. 8G.

FIG. 9 shows a diagram of an exemplary embodiment of a wireless powersystem.

FIGS. 10A, 10B, 10C, and 11 show flowcharts of exemplary embodiments ofcontrol schemes for tuning wireless power receivers.

FIGS. 12A-12B are flowcharts of exemplary methods for adjusting acapacitance values of capacitor C₂ in a wireless power receiver having acontroller. FIG. 12C is a flowchart of an exemplary method for producingthe desired capacitance value C_(2_desired) of FIGS. 12A-12B.

FIG. 13 is a plot of voltage at load resistance R_(load) of 30Ω as afunction of capacitance values of C₂ and C₃.

FIG. 14A is a flowchart of an exemplary method for tuning based on afunction. FIG. 14B is an exemplary function of voltage V_(AC) as afunction of capacitance C₂ and C₃ of a load resistance R_(load) of 20 Ω.

DETAILED DESCRIPTION

Voltage induced across receiver resonator coils can be loaded byreceiver circuitry. Typically, the receiver resonator is coupled to animpedance matching network (IMN), a rectifier (passive or active),filtering, and a regulating converter producing a desired parameter(e.g. DC-DC voltage regulator presenting a fix voltage supply to aload). Battery chargers are a special example where power is typicallyregulated. A local control loop (either feedforward or feedback) can beused. However, additional regulation stages, such as a DC-DC converter,can add power loss and complexity. In some embodiments, a preferredalternative may be regulation via the IMN (utilizing tunable elements)and/or active rectifiers.

Multiple tuning elements performing regulation of various parameters canremove the need for additional costly or bulky regulation circuitrywhich can ultimately lower efficiency of power transmission to the loador battery of an electronic device. Examples of electronic devicesinclude cell phones, laptops, tablets, fitness devices, watches, and thelike. Tuning elements can also decrease sensitivity to manufacturingtolerances, environmental effects (such as temperature), and othervarying parameters. Care must be taken that controlling the tuningelement does not cause more loss, greater EMI issues, etc. thatcounteract the benefit of tuning. Using multiple, high Q (qualityfactor) tuning elements, such as barium strontium titanate (BST)capacitors, can maintain high efficiency while performing regulation aswell. Using high speed tuning elements like the PWM capacitor can havevery fast transient response.

Key metrics of voltage or power regulation in the receiver circuitryinclude transient response, steady-state error, transmitter driveefficiency, power dissipation in receiver (thermals, productrequirement, safety), non-linear distortion (electromagneticinterference (EMI)—radiated and conducted). Transient responses, whichcan be caused by load changes, changes in coupling, temperature drift,etc., necessitate some degree of compensation speed that may beimplementation dependent. For example, the speed of control loops andcommunication between parts of the receiver and/or transmitter may limitthe speed of response. Details of illustrative embodiments are discussedbelow.

System Description

FIG. 1 shows a diagram of an exemplary embodiment of a wireless powertransmission system including a wireless power transmitter 102 andwireless power receiver 104. The wireless power transmitter 102 includesa full-bridge differential RF inverter 106 coupled to a transmitterimpedance matching network (IMN) 108 and a transmitter resonator coil110. The wireless power receiver 104 includes a receiver resonator coil112 coupled to a receiver IMN 114 and an RF rectifier 116. The receiver104 may be coupled directly to a load such as a battery or batterymanager of an electronic device. Note that the components of thetransmitter IMN 108 and/or receiver IMN 114 may be tunable. Further, theinverter 106 and/or rectifier 116 may be tunable. For example, theswitches (S_(T1), S_(T2), S_(T3), S_(T4)) of the inverter 106 and/orswitches (S_(R1), S_(R2), S_(R3), S_(R4)) of the rectifier 116 may becontrollable by controllers 118 and 120, respectively, to achievevariable dead-time, phase-shifting, etc.

FIG. 2 shows a diagram of an exemplary embodiment of a wireless powertransmission system including a wireless power transmitter 202 andwireless power receiver 204. The wireless power transmitter 202 includesa full bridge differential RF inverter 206 coupled to a transmitterimpedance matching network (IMN) 208 and a transmitter resonator coil210. The wireless power receiver 204 includes a receiver resonator coil212 coupled to a receiver IMN 214 and an RF rectifier 216. The receiver204 may be coupled directly to a load such as a battery or batterymanager of an electronic device. Note that the components of thetransmitter IMN 208 and receiver IMN 214 may be tunable. In someembodiments, IMN 208 can include a tunable or fixed shunt cap 218 for adifferential class E or F inverter. Further, the inverter 206 and/orrectifier 216 may be tunable. For example, the switches (S_(T1), S_(T2))of the inverter 206 and/or switches (S_(R1), S_(R2), S_(R3), S_(R4)) ofthe rectifier 216 may be controllable by controller 218 and 220,respectively, to achieve variable dead-time, phase-shifting, etc.

FIG. 3A shows an exemplary embodiment of a wireless power receiverincluding a receiver resonator coil 302 coupled to one or morecapacitors and impedance matching components 304, one or more diodes306, active clamp 308, inductors 309A and 309B, smoothing capacitor 310,load 312, one or more sensors 314, controller 316, and a wirelesscommunication module 318. In some embodiments, the wirelesscommunication module 318 may be a wireless communication device (forexample, Bluetooth Low Energy (BLE)) available on the electronic device320 to which the receiver 322 is coupled. The active clamp 308 can beused as a circuit protection measure to ensure that voltage does notincrease above a predetermined limit. The inductors 309A and 309B areused to filter out common-mode signals. The smoothing capacitor 310 cansmooth ripple or variations in output rectifier voltage. In someembodiments, the connection between the controller and the BLE can bemediated via serial peripheral interface ports 324, 326 on the receiver322 and electronic device. In some embodiments, the impedance matchingcomponents 304 may be variable capacitors, such as BST capacitors, PWMcontrolled capacitors, bank of capacitors, and the like. In someembodiments, the one or more diodes used to rectify the oscillatingenergy captured at the receiver resonator coil may be Schottky diodes.It can be advantageous to use Schottky diodes due to their low forwardvoltage drop and fast switching. Note that Schottky diodes can be usedon one leg (top) of the circuit while the other leg is a short. Thisimbalanced loading approach can decrease complexity and cost of thecircuit. In some embodiments, sensors can be used to sense current,voltage, and/or power along the current pathways within the receiver. Anadvantage to this system is that the voltage regulation is achieved atthe IMN of the receiver, avoiding the use of a DC-DC converter. In someembodiments, one or more of the components coupled to the receiverresonator coil can be co-packaged into an application-specificintegrated circuit (ASIC) 328. For example, an ASIC may include one ormore impedance matching components 304, one or more diodes 306, activeclamp 308, sensors 308, controller 316, and/or a wireless communicationmodule.

FIG. 3B shows an exemplary embodiment of a wireless power receiverincluding many of the components listed above for FIG. 3A. Some of thedifferences are described in the following. For example, the receiver330 includes a “split-coil” receiver resonator coil 332. The split coilis coupled to capacitor configuration 334 that is connected to ground.This configuration can mitigate common-mode (CM) signal issues. Notethat the tuning of the top capacitor can be independent from the bottomcapacitor.

FIG. 4 shows an exemplary embodiment of a wireless power receiverincluding a receiver resonator coil 402 coupled to one or morecapacitors and impedance matching components 404, a rectifying diodebridge 406, a controller/wireless communication module 408, inductors409A and 409B, and a smoothing capacitor 410. The receiver 412 iscoupled to a load 414 of an electronic device. In some embodiments, thediode bridge 406 can be a full-bridge rectifier having Schottky diodes.In some embodiments, the one or more components coupled to the receiverresonator coil 402 can be co-packaged into an ASIC 416.

Receiver Description

FIG. 5 shows an exemplary embodiment of a wireless power receiverincluding one or more receiver resonator coils 502, 504 coupled to oneor more capacitors 506, 508 and a rectifier 510 with an output to aload. The receiver resonator coils 502, 504 can be switched in and outto be in parallel or series and result in a different overallinductance. For example, when switch A is closed (and switches B, C areopen), the coils 502, 504 are coupled in series. When switches B and Care closed (and A is open), the coils 502, 504 are coupled in parallel.Further, each of the coils 502, 504 can be activated independently byclosing either switch B or C. The capacitors 506, 508 can be tunablecapacitors. In some embodiments, the switches, capacitors, and rectifiercan be packaged into an integrated circuit (such as an ASIC). In someembodiments, the rectifier may be an active rectifier using switches.

In exemplary embodiments, a wireless power receiver can include areceiver resonator coil coupled to a network of capacitors. In someembodiments, the network capacitors can include one or more switch orPWM controlled capacitors. These switch controlled capacitors may beactivated when the wireless power transmission system is operating atlower frequencies, such as 100-300 kHz. In some embodiments, thecapacitors can include one or more BST capacitors. The BST capacitorscan be designed or chosen to have a quality factor Q_(cap) equal to orgreater than the quality factor of the resonator coil Q_(coil). Thesetunable capacitors may be activated when the wireless power transmissionsystem is operating at higher frequencies, such as 1 MHz to 2.4 GHz (forexample, 6.78 MHz or 13.56 MHz). In some embodiments, the switched ortunable capacitor can be configured to operate at any ISM (Industrial,Scientific, or Medical) frequency band. This may allow the system toswitch from one mode, for example, at 120 kHz, to another mode, at 6.78MHz and have tuning capability at each of these modes.

FIG. 6A shows an exemplary embodiment of a wireless power receiver 600including a receiver resonator coil 602 coupled to a network ofcapacitors 604 and a rectifier 606 with an output to a load. The networkof capacitors 604 can include any of the above described discrete orcontinuous tunable capacitors. In this example, a first subcircuitincludes coil 602 coupled in series with capacitors C_(1A), C_(1B),C_(1C), C_(1D). A second subcircuit includes the first subcircuitcoupled in parallel to capacitors C_(2A), C_(2B). A third subcircuitincludes the second subcircuit coupled in series with capacitors C_(3A),C_(3B), C_(3C), C_(3D). This third subcircuit is coupled into arectifier 606.

Note that capacitors C_(1A) and C_(1B) are connected in parallel to oneanother in the same position relative to coil 602. In some embodiments,capacitor C_(1A) may be a discrete tunable capacitor while capacitorC_(1B) may be continuous tunable capacitor. This can provide both“coarse” and “fine” tuning for a capacitance at position C₁. In someembodiments, capacitor C_(1A) may be a type of capacitor that is suitedfor tuning at frequency or group of frequencies f₁ and capacitor C_(1B)may be a type of capacitor that is suited for tuning at frequency orgroup of frequencies f₂. For example, if the wireless power receiver 600detects, via wireless communication or impedance measurement, atransmitter capable of transmitting power at frequency f₁, then thereceiver 600 may switch in capacitor C_(1A) (and may keep capacitorC_(1B) switched out). If the receiver 600 detects a transmitter capableof transmitting power at frequency f₂, then the receiver 600 may switchin capacitor C_(1B) (and may keep capacitor C_(1A) switched out).Similar embodiments are relevant for each of the capacitors connected inparallel (C_(1C) and C_(1D), C_(2A) and C_(2B), C_(3A) and C_(3B),C_(3C) and C_(3D)). Note that capacitors C_(1A) and C_(1B) are balancedwith C_(1C) and C_(1D). This can mitigate common mode signal issues. Insome embodiments, one or more of these components along with therectifier 608 may be packaged into an integrated circuit 610.

In some embodiments, the capacitors in network 604 can include one ormore switch or PWM controlled capacitors, respectively. These switchcontrolled capacitors may be activated when the wireless powertransmission system is operating at lower frequencies, such as 100-300kHz. In some embodiments, the capacitors in network 604 can include oneor more BST capacitors, respectively. The BST capacitors can be designedor chosen to have a quality factor Q_(cap) equal to or greater than thequality factor of the resonator coil Q_(coil). These tunable capacitorsmay be activated when the wireless power transmission system isoperating at higher frequencies, such as 1 MHz-2.4 GHz (for example,6.78 MHz or 13.56 MHz). In some embodiments, the switched or tunablecapacitor can be configured to operate at any ISM (Industrial,Scientific, or Medical) frequency band. This may allow the system toswitch from one mode, for example, at 120 kHz, to another mode, at 6.78MHz and have tuning capability at each of these modes. For example,capacitor C_(1A) may be a PWM controlled capacitor with f1=100-300 kHzand capacitor C_(1B) may be a BST capacitor with f2=1 MHz-2.4 GHz.

FIG. 6B shows an exemplary embodiment of a wireless power receiver 608including a “split” receiver resonator coil 602A, 602B coupled to anetwork of capacitors 612 and a rectifier 614 with an output voltageV_(rect) to a load. In this example, a first subcircuit includes coil602A, 602B coupled in series with capacitors C_(1E), C_(1F). A secondsubcircuit includes the first subcircuit coupled in parallel tocapacitors C_(2A), C_(2B). A third subcircuit includes the secondsubcircuit coupled in series with capacitors C_(3A), C_(3B), C_(3C),C_(3D). This third subcircuit is coupled into a rectifier 606. Note thatcapacitors C_(1E) and C_(1F) are connected in parallel to one another.As described above for capacitors C_(1A) and C_(1B), C_(1E) and C_(1F)can be different types of capacitors or can be configured to beactivated or switched in at different frequencies. In some embodiments,particular sets of capacitors may be switched in or out based on thedetection of a protocol or standard of wireless power transmission thatthe transmitter utilizes.

Tuning Configurations

FIG. 7 shows an exemplary embodiment of a receiver 700 with a tunableimpedance matching network. The receiver 700 includes a resonator coil702 coupled in series to capacitor C₁. Next, connected in parallel tothe resonator coil and C₁, is a voltage sensor 704 that measures voltageV₁. The differential voltage measurements V_(c1), V_(c2) are fed intointegrator INT. In some embodiments, a peak detector PD is used todetect the amplitude P (as function of time) of the measured voltagesignal V₁. The voltage signal is also fed into a mixer (SIN and COS) andone or more filters (LPF) to detect the phase of the voltage signal V₁.Refer to the “Mixer Operation” section below for description related tothe function and outputs of phase detection. The amplitude and phasemeasurements can be used by a controller to tune system components, suchas the tunable capacitors C₁, C₂, and C₃, or control other parts of thereceiver, such as rectification or safety mechanisms.

Next, coupled in parallel to the voltage sensor 704 is capacitor C₂. Acurrent sensor 706 can be positioned between voltage sensor 704 andcapacitor C₂ to measure coil current I_(coil). Coupled in series to theC₂ is a capacitor C₃. A current sensor 708 can be positioned between C₂and C₃ to measure current I₃. Each of these current sensors 706 and 708can be connected to amplitude and phase measurement circuits asdescribed above for voltage sensor 704. Coupled in series to capacitorC₃ is inductor L′₃ (balanced) and rectifier 710. In some embodiments,the rectifier 710 can be an active rectifier, such as a synchronousrectifier. The rectified voltage output V_(rect) may be fed directly toa load or though other circuitry, such as voltage clamps or filters (seeFIGS. 3A, 3B, and 4).

In some exemplary embodiments, tunable capacitors C₁, C₂, and C₃ may becontrolled by a controller 712. Note that the outputs of the varioussensors 704, 706, and 708 can be fed into component 712. The controller712 in addition to some or all of components INT, PD, SIN and COS, andLPF may be integrated into an integrated circuit 714, such as an ASIC.

Mixer Operation

The input signal may be a signal representing a measured current orvoltage at a location within a power transfer system. The input signalmay be, for example, a voltage signal representing a measured current orvoltage at a location within a power transfer system, and can berepresented by A_(IN)·sin(ωt+φ), where φ is the phase of the inputsignal relative to the reference signals. For example, the input signalcan be the output of a Rogowski coil positioned within the circuitry ofa power transfer system to measure a current signal.

The signal mixers are coupled with the signal supply (such as thevoltage signal V₁) so as to receive one of the reference signals as oneinput and the input signal as another input. The mixers (SIN and COS)mix (e.g., perform time-domain multiplication) a respective referencesignal with the input signal and output mixed signal 1 and 2. Thus,mixed signal 1 can be represented by:

${Q = {{A_{IN}*{\sin\left( {{\omega\; t} + \varphi} \right)}*A*{\sin\left( {\omega\; t} \right)}} = {{\frac{AA_{IN}}{2}*{\cos(\varphi)}} - {\frac{AA_{IN}}{2}*{\cos\left( {{2\omega\; t} + \varphi} \right)}}}}},$and mixed signal 2 can be represented by:

$I = {{A_{IN}*{\sin\left( {{\omega\; t} + \varphi} \right)}*A*{\cos\left( {{\omega\; t} + \theta} \right)}} = {{\frac{AA_{IN}}{2}*{\sin\left( {\varphi - \theta} \right)}} + {\frac{AA_{IN}}{2}*{{\sin\left( {{2\omega\; t} + \varphi + \theta} \right)}.}}}}$

Filters (LPF) can be low-pass filters designed to filter, for example,the second harmonic from the first and the second mixed signal that isgenerated by the mixers. Accordingly, the filters may remove the secondorder harmonics generated from the signal mixing process as well as anyhigher order harmonics that were present in either reference signals orthe input signal. After filtering, mixed signal 1 can be represented by:

${Q = {\frac{AA_{IN}}{2}*{\cos(\varphi)}}},$and mixed signal 2 can be represented by:

$I = {\frac{AA_{IN}}{2}*{{\sin\left( {\varphi - \theta} \right)}.}}$

The controller receives the mixed signals Q and I, determines the phaseof the input signal, and outputs the phase of the input signal to, forexample, IMN control circuitry. Impedance at the operating frequency canbe determined using a ratio of Q to I. In some embodiments, theimpedance can be input to detection algorithms such as rogue objectdetection, foreign object detection, RFID detection, proximitydetection, coil alignment, and the like.

Exemplary Relationships

FIG. 8A shows a receiver resonator coil L₁ coupled in series to atunable capacitor C₁. The foregoing circuit is coupled to a rectifier802 with an output of a rectified voltage V_(rect,1). FIG. 8B showsrectified voltage as a function of tuning C₁ for the circuit of FIG. 8Acoupled to a load at the output 804 of the rectifier. Note that the peakof the rectified voltage V_(rect,1) can be at most the voltageV_(peak,1) induced by the transmitter on the receiver resonator coil L₁.This condition may be met when inductor L₁ is at resonance withcapacitor C₁, when impedance is at its lowest. For example, ifV_(rect,1) is too high, C₁ may be tuned away or detuned from resonancewith L₁ to decrease V_(rect,1).

FIG. 8C shows a receiver resonator coil L₁ coupled in parallel tocapacitor C₂. The foregoing circuit is coupled to a rectifier 802 withan output of a rectified voltage V_(rect,2). FIG. 8D shows thatrectified voltage V_(rect,2) is at its maximum V_(peak,2) when capacitorC₁ is at resonance with inductor L₁ for the circuit of FIG. 8C coupledto a load at the output 804 of the rectifier. Note that:V _(peak,2) >>V _(peak,1)

Thus, this circuit can be considered a “boost” to the voltage suppliedby the transmitter. In some embodiments, rectified voltage V_(rect,2)may be too large and an additional series element, such as capacitor C₁,as shown in FIG. 8E, or capacitor C₃, as shown in FIG. 8G, may beutilized. FIG. 8E shows a receiver resonator coil L₁ coupled in serieswith capacitor C₁ and in parallel with capacitor C₂. The foregoingcircuit is coupled to a rectifier 802 with an output of a rectifiedvoltage V_(rect,3). Note that capacitors C₁ and C₂ can be used resonatewith L₁ in different ratios. Similarly, these capacitors can be used todetune the resonator in different ratios.

FIG. 8F shows an equivalent circuit for FIG. 8E where L′₁ is the seriesequivalent of inductance L₁ and capacitance C₁:

$Z_{series\_ equiv} = {{Z_{L1} + Z_{C\; 1}} = {{{j\omega L_{1}} + \frac{1}{j\omega C_{1}}} = {j\;\omega\;{L_{1}^{\prime}.}}}}$Inductance L′₁ is less than inductance L₁ leading to a lower rectifiedvoltage. Overall, the peak V_(peak,3) of rectified voltage V_(rect,3)can be approximately described by the following:V _(peak,2) ≥V _(peak,3) ≥V _(peak,1)When inductor L₁, capacitor C₁, and capacitor C₂ are at resonance,V_(rect,3) increases with an increase in C₁. Note that capacitance C₂has a correlating decrease with an increase in C₁. For example, thisrelationship can be determined by voltage division:

$V_{{rect},3} = {V_{L1} \cdot \frac{Z_{C2}}{Z_{C2} + Z_{C1}}}$where V_(L1) is the voltage at the node between inductor L₁ andcapacitor C₁. Simplifying the above using equalities

$Z_{C1} = \frac{1}{j\;\omega\; C_{1}}$and Z_(C2)=1/jωC₂, is shown that V_(rect,3) is proportional to C₁:

$V_{{rect},3} = {V_{L1} \cdot {\frac{C_{1}}{C_{1} + C_{2}}.}}$

FIG. 8G shows a receiver resonator coil L₁ coupled in parallel to C₂.Coil L₁ and C₂ are coupled in series to C₃. The foregoing circuit iscoupled to a rectifier 802 with an output of a rectified voltageV_(rect,4). As described for the above circuits, parallel capacitor C₂can boost the rectified voltage. In some embodiments, series capacitorC₃ can compensate for a varying load.

FIG. 8H shows an equivalent circuit for FIG. 8G where L′₁ is theparallel equivalent of inductance L₁ and capacitance C₂:

$Z_{parallel\_ eqiv} = {\frac{Z_{L1}Z_{C2}}{Z_{L1} + Z_{C2}} = {\frac{j\omega L_{1}*\frac{1}{j\;\omega\; C_{2}}}{{j\omega L_{1}} + \frac{1}{j\;\omega\; C_{2}}} = {\frac{j\omega L_{1}}{{{- \omega^{2}}L_{1}C_{2}} + 1} = {j\;\omega\;{L_{1}^{''}.}}}}}$Inductance L″₁ is greater than inductance L₁ leading to a higherrectified voltage. Note that capacitor C₃ in the receiver matchingnetwork can maximize the current to the load. In some embodiments, thetuning of capacitor C₃ in the receiver matching network can increase ordecrease the overall Thevenin output impedance of the receiver. Atunable capacitor C₃ can also be used to compensate for the detuning ofinductor L₁. Overall, the peak V_(peak,4) of rectified voltageV_(rect,4) can be approximately described by the following:V _(peak,2) ≥V _(peak,4) ≥V _(peak,1).When inductor L₁, capacitor C₂, and capacitor C₃ are at resonance, anunloaded V_(rect,4) increases with an increase in C₂ until the value ofC₂ is equal to a resonating capacitance C_(2_resonant). A loaded Vrect,4increases and decreases before C2 reaches the resonating valueC2_resonant (see FIG. 13). Note that capacitance C₃ has a correlatingdecrease with an increase in C₂. For example, the sum capacitance C₂+C₃can remain approximately constant while adjusting C₂ and C₃. A higherrectified voltage can be achieved from higher C₂ and lower C₃ values fora C₂ value less than C_(2,critical). C_(2,critical) can be defined asthe capacitance that maximizes the voltage independent of powerefficiencies.

In some embodiments, the receiver-side capacitors are kept tuned toresonance to maximize efficiency. In some embodiments, if the receiveris detuned, the receiver-side capacitors may be retuned as a first step.If resonance cannot be achieved at the receiver, then the receiver maycommunicate with the transmitter to tune the transmitter-sidecapacitors.

Control Schemes

FIG. 9 shows an exemplary embodiment of a wireless power receiver 900receiving wireless power from a power transmitter 902. The receiverincludes a receiver resonator coil L₁, impedance matching network (IMN)904, rectifier 906, and controller 908. In some embodiments, thecontroller 908 includes a processor 909. In some embodiments, thecontroller 908 can be coupled to a processor 909. The receiver can becoupled to a load 910 in an electronic device such as the battery of acell phone, laptop, tablet, and the like. In some embodiments, thecontroller 908 can be coupled to sensors (such as current and voltagesensors) that provide measurements to a control loop. In someembodiments, the controller 908 can tune elements of the IMN 904 toregulate the power to the load 910 and/or achieve high efficiency powertransmission to the load 910. The controller 908 can be integratedwithin or coupled to a wireless communication module (such as aBluetooth module). In some embodiments, a voltage clamp can be includedfor start-up conditions (for example, with a large initial spike involtage) and potential error conditions.

The exemplary system utilizes a feedback loop to control components ofthe IMN 904 of the wireless power receiver 900 to optimize the powerefficiency of the receiver. The components of the IMN 904 can beinductors and/or capacitors and the value of these components can bechanged in a discrete or continuous fashion. One implementation of thisapproach is where the IMN is formed with variable capacitors, such asBST capacitors, PWM-controlled capacitors, or another implementation iswhere the IMN is formed with an array or bank of discrete capacitorsusing switches to change the value of the capacitance.

Tuning Loop #1: Maximize System Efficiency

FIG. 10A shows an exemplary embodiment of a control loop to tune thereceiver IMN 904. In some exemplary embodiments, the tunable IMN can becontrolled by a control loop that includes feedback information from thewireless power transmitter 902 and information at the receiver load 910to optimize the system efficiency. System efficiency can be defined asthe ratio of power into the load at the receiver to input power at thetransmitter, P_(load)/P_(in). The control loop can change the componentsof the receiver IMN 904 such that the efficiency P_(load)/P_(in) ismaximized. For example, a voltage, current, or power sensor at the inputpower to the transmitter can measure or calculate input power. Avoltage, current, or power sensor at the input to the load 910 canmeasure or calculate output power. A processor within a controller orcoupled to the controller can calculate system efficiency using theabove ratio. The controller can, in response, adjust the components C₂and/or C₃ of the receiver IMN 904.

In another example, in a first step 1002, if other measurements areknown (such as resistance of the transmitter coil) current I₁ in thetransmitter resonator coil can be measured and an input powerP_(in,Tx_coil) can be calculated. The output voltage V_(out) can bemeasured at the receiver load 910 and output power P_(load) can becalculated using an additional current or resistance measurement. In asecond step 1004, the processor can calculate the system efficiency bytaking the ratio P_(load)/P_(in,Tx_coil). In a third step 1006, thecontroller can, in response, adjust the components C₂ and/or C₃ of thereceiver IMN 904. In some embodiments, the controller can adjust C₂ andmeasure the effect on the output voltage. If the outcome is not desired,the controller may return C₂ to its previous value and/or adjust C₃ andmeasure the effect on the output voltage until a desired outcome isachieved.

Tuning Loop #2: Maximize Power Delivered to the Load

FIG. 10B shows an exemplary embodiment of control loop to tune thereceiver IMN 904. In some exemplary embodiments, a receiver control loopcan maximize power delivered to the load 910. This can be as part of thecontrol loop in maximizing system efficiency or a local control loop atthe receiver. If the power transmitted from the wireless powertransmitter is approximately constant, then the receiver can have alocal control loop to maximize P_(load). This can decrease complexityand computational effort. Note that the feedback loop can be implementedin an analog, digital, or mixed-signal (analog and digital) circuitswith or without a controller. In a first step 1008, voltage, current, orpower can be measured or calculated at the input to the load 910. In asecond step 1010, the efficiency of the receiver can be calculatedassuming that a constant current at the transmitter. In anotherembodiment, the efficiency of the receiver can be calculated by taking avoltage, current, and/or power measurement at the receiver resonatorcoil and calculating an input power P_(in,Rx_coil) and comparing toP_(load). In a third step 1012, the controller can, in response, adjustthe components C₂ and/or C₃ of the receiver IMN 904.

Tuning Loop #3: Achieve Target Voltage for the Load

FIG. 10C shows an exemplary embodiment of control loop to tune thereceiver IMN 904. In some exemplary embodiments, a receiver control loopcan tune the IMN 904 to hit a target voltage V_(target) for the load910. For example, a target voltage V_(target) could be a voltage at ornear the maximum input voltage V. of the load 910. By driving thewireless power receiver output to the maximum input voltage V. of theload (such as a battery charger input), the wireless power receiverefficiency is optimized. Also, with such a control technique, the use ofa DC-to-DC converter can be avoided and thus, the efficiency of thewireless power receiver can be further optimized. In other words, thelosses that may be attributable to a DC-to-DC converter may be avoided.An advantage of tuning the receiver IMN 904 based on the load voltage isthat the rectifier output can be ensured to be in a safe operatingregion. The safe operating region can be ensured because the feedbackloop is adjusting the IMN 904 components such that the rectifier outputachieves the target load voltage V_(target).

For example, assume the load of the wireless power receiver is a batterycharging integrated circuit with a maximum input voltage of 20V. Thetarget load voltage V_(target) ideally can be 20V but will likely be setto a lower voltage, for example 19V, due to ripple and othernon-idealities coming from the rectifier. The controller 908 on thewireless power receiver can be a negative feedback loop that regulatesthe rectifier output voltage to the target load voltage. The loop wouldcompare the rectifier output voltage and compare it to the targetvoltage, in this example 19V, to generate an error signal. This errorsignal would then change the components of the IMN 904 (for example,capacitors C₂ and C₃) such that the rectifier output voltage is equal tothe target voltage, resulting in no error signal. Implementation of thefeedback loop can be implemented in the analog domain using operationalamplifiers and PWM signals with variable capacitors and/or in the mixedsignal analog and digital domain using analog-to-digital converters,comparators, microcontrollers, digital logic, firmware, switches andcapacitor banks. In some embodiments, a combination of continuouslyvariable capacitors for fine tuning while switches and capacitor bankscan be used for coarse tuning. For example, if the wireless powerreceiver can be embedded into a pre-defined system, for example alaptop, cell phone, etc., the target voltage can be known a priori andcan be easily inputted or programmed into the controller or memory unit.In some embodiments, the target voltage does not need to be static andcan be changed, for example, by a user of the system or different safetyconditions.

FIG. 11 shows an exemplary embodiment of a control scheme for theregulation of rectified voltage of a wireless power receiver. Inputs tothis control scheme can come from measurements (i.e. from sensors) ofrectified voltage V_(rect), currents I₁, I₂, I₃ (see FIG. 7), and/orvoltages in the matching network. At step 1102, rectified voltage ismeasured and, at step 1104, compared to a target voltage V_(target),within some error, hysteresis, or approximation interval±ε. In someembodiments, target values of rectified voltage can be 1V, 5V, 10V, and20V in consumer electronics such as mobile electronics and laptops. Insome embodiments, this interval c can be 1%, 5%, 10%, or more of targetvoltage V_(target). For example, for an analog voltage measurement, thisinterval can be 10-100 mV in a 10V system. If the voltage measurement isa digital signal, comparison of V_(rect) to V_(target) can depend onnumber of bits or quantization, at or above noise floor.

If V_(rect) is less than V_(target)−ε, at step 1106, reactance X₂ ofcapacitor C₂ is compared to a minimum reactance value X_(2,min). If X₂is less than or equal to X_(2,min), at step 1108, transmitter currentI_(TX) can be increased. In some embodiments, the receiver can signalthe transmitter to increase I_(TX). In some embodiments, the transmittercan detect the measurements at the receiver and adjust current I_(TX)accordingly. This may be accomplished by sending a control signal fromthe receiver to the transmitter. In some embodiments, the transmittermay be monitoring the receiver and may sense this condition. Oncecurrent I_(TX) is increased, V_(rect) can be measured at step 1102. IfX₂ is greater than X_(2,min), at step 1110, X₂ can be decreased, forexample, by tuning capacitor C₂. At step 1112, V_(rect) is monitored andat step 1114, reactance X₃ of capacitor C₃ is increased. For example, iftuning of C₃ is discrete (i.e. via a bank of capacitors) and increasingX₃ causes V_(rect) to be out of the hysteresis band ε, steps 1110 to1114 may be cycled through to stabilize V_(rect). Control passes back tostep 1102.

At step 1104, if V_(rect) equals V_(target) within ±ε and reactance X₂does not equal maximum reactance X_(2,max), then control passes back tostep 1102.

At step 1104, if V_(rect) is greater than V_(target)+ε, then X₂ iscompared to maximum reactance X_(2,max) at step 1116. If X₂ is less thanX_(2,max), at step 1118, X₂ is increased. Control passes back to step1116. If X₂ is greater or equal to X_(2,max), at step 1120, reactance X₃is compared to X_(3,min). If X₃ is greater than X_(3,min), at step 1122,X₃ is decreased and control passes back to V_(rect). If X₃ is less thanor equal to X_(3,min), at step 1124, transmitter current I_(TX) can bedecreased. In some embodiments, the receiver can signal the transmitterto increase I_(TX). In some embodiments, the transmitter can detect themeasurements at the receiver and adjust current I_(TX) accordingly.

Tuning Loop #4: Regulate Rectified Voltage V_(Rect)

In some embodiments of a wireless power receiver, the rectified voltagemay be regulated by adjusting the capacitance value of the one or morecapacitors in position C₂ (see at least FIG. 8C, 8E, or 8G). Theadjustment value may depend on the maximum dissipation power allowed inthe receiver resonator, of which capacitor C₂ is a part. FIG. 12A is aflowchart of an exemplary method for a wireless power receiver having acontroller. Note that each of the following steps can be executed by thecontroller coupled to components of the receiver. Examples of suchcontrollers are shown in at least FIGS. 1-4, 7, and 9. Step 1202receives, at a first input of the controller, a value signalrepresentative of a rectified voltage V_(rect). Step 1204 operates, in aprocessor coupled to the first input, on the signal representative ofthe rectified voltage V_(rect) to produce a desired capacitance valueC_(2_desired) for capacitor C₂. Step 1206 provides, via a first outputof the controller, an adjustment signal so as to adjust a capacitancevalue C_(2_value) of capacitor C₂ to the desired capacitance valueC_(2_desired).

FIG. 12B is a flowchart of an exemplary method for a wireless powerreceiver having a controller that includes steps 1202-1206. Theexemplary method also includes in step 1208 which compares, by theprocessor, the signal representative of the rectified voltage V_(rect)to a range of voltages defined by an upper limit V_(upper) and lowerlimit V_(lower), the range of voltages stored in a memory of thecontroller. Step 1210 transmits, via the first output of the controller,the adjustment signal to the tunable capacitor C₂ in response to thecomparison of the signal representative of the value of rectifiedvoltage V_(rect) to the range of voltages.

FIG. 12C is a flowchart of an exemplary method for producing the desiredcapacitance value C_(2_desired) of step 1204 in FIGS. 12A-12B. Step 1212receives at a second input of the controller, a signal representative ofa rectified current I_(rect). I_(rect) can be sensed, measured, orcalculated at the output of the rectifier of the receiver. Step 1214operates, in the processor, on the signals representative of each of therectified voltage V_(rect) and current I_(rect) to determine power P_(L)to a load coupled to the rectifier output and resistance R_(L) at theload. For example, the power P_(L) and resistance R_(L) can becalculated from these measurements:R _(L) =V _(rect) /I _(rect)P _(L) =I _(rect) ·V _(rect).

Step 1216 operates, in the processor, on the receiver resistanceR_(receiver) and power P_(L) to determine power P_(receiver) to thereceiver. Receiver resistance R_(receiver) and power to the receiverP_(receiver) can be determined by:

R_(receiver) = ω ⋅ L₁/Q$U_{d} = \frac{R_{l}C_{3}^{2}}{\left( {\left( {C_{2} + C_{3}} \right)^{2} + {\omega^{2}R_{l}^{2}C_{2}^{2}C_{3}^{2}}} \right)R_{d}}$P_(receiver) = P_(L)(U_(d) + 1),where U_(d) is a figure-of-merit for the receiver.

Step 1218 operates, in the processor, on power P_(receiver), a value ofcapacitor C₂, and a value of capacitor C₃ to determine an open circuitvoltage value V_(open), wherein the desired capacitance valueC_(2_desired) is a function of V_(open). The values of capacitors C₂ andC₃ can be a most recent measurement or estimation.

To calculate V_(open), the Thevenin impedance Z_(th) of receiver circuitis determined:

$Z_{th} = {Z_{3} + \frac{\left( Z_{1} \right)\left( Z_{2} \right)}{Z_{1} + Z_{2}}}$where Z₁ = R₁ + jωL₁ $Z_{2} = {R_{2} + \frac{1}{j\omega C_{2}}}$$Z_{3} = {R_{3} + {\frac{1}{j\omega C_{3}}.}}$From the Thevenin impedance, the AC-side voltage is determined:

$V_{AC} = {\frac{V_{L}Z_{th}}{R_{L}}.}$

Thus, the open circuit voltage value V_(open) can be determined by:

$V_{open} = {V_{th} = \frac{V_{ac}}{{j\omega C_{2}R_{d}} - {\omega^{2}L_{d}C_{2}} + 1}}$Thus, to produce the desired capacitance value C_(2_desired) of step1204 in FIGS. 12A-12B:

${C_{2{\_ desired}} = \frac{{2\omega^{2}L_{d}} \mp \sqrt{{4\omega^{4}L_{d}^{2}} - {4\left( {{\omega^{4}L_{d}^{2}} + {\omega^{2}R_{d}^{2}}} \right)\left( {1 - \left( \frac{Vac}{Vopen} \right)^{2}} \right)}}}{2\left( {{\omega^{4}L_{d}^{2}} + {\omega^{2}R_{d}^{2}}} \right)}}.$

Note that, in some embodiments, the maximum capacitance value of C₂ canbe determined by the following:

${C_{2{\_ max}} = \frac{{2\omega^{2}L_{d}} \mp \sqrt{{4\omega^{4}L_{d}^{2}} - {4\left( {{\omega^{4}L_{d}^{2}} + {\omega^{2}R_{d}^{2}}} \right)\left( {1 - \left( \frac{Vac}{Vocmax} \right)^{2}} \right)}}}{2\left( {{\omega^{4}L_{d}^{2}} + {\omega^{2}R_{d}^{2}}} \right)}}.$where V_(ocmax) is the maximum open circuit voltage value that isdependent on the circuit. It can be helpful to determine the maximumcapacitance value C_(2_max) such that the value of capacitor C₂ has anupper limit. This may mitigate any potential harm or damage from highvoltages in the receiver. In some embodiments, the value ofC_(2_desired) can equal the value C_(2_max).

In some embodiments, once having determined the desired value forcapacitor C₂, a desirable value for capacitor C₃ can be determined withthe goal of obtaining a rectified voltage V_(rect) within a range ofV_(upper) and V_(lower). In an exemplary embodiment, the capacitancevalue of C₃ can be determined by a lookup table that stores the valuesof C₂, C₃ pairs. FIG. 13 is a plot of AC load voltage V_(AC_load) atload resistance R_(load) of 30Ω as a function of capacitance values ofC₂ and C₃. Note that the relationship between AC load voltageV_(AC_loaded) is as follows:

$V_{AC\_ loaded} = {\frac{2\sqrt{2}}{\pi}{V_{rect}.}}$

A lookup table derived from this function, and stored in the memory of acontroller, can be accessed by a processor to provide adjustment valuesfor tunable capacitor C₃. Note that, in this embodiment, the approximaterelationship between C₂ and C₃ is that, for a higher desired voltage,the adjustment signal for capacitor C₂ from the processor would beconfigured to increase the capacitance value of C₂ (within a limit1304). The adjustment signal for capacitor C₃ would be configured todecrease the capacitance value of C₃ (within a limit 1304).

In some embodiments, the known values of capacitors C₂ and C₃ can befurther refined or observed by using the induced voltage, open circuitconditions, known power to the receiver, and loading condition at thereceiver load. Knowing the open circuit voltage of the output of therectifier can lead to the value of capacitor C₂ by the followingrelationships:

V_(Open_Circuit) = A_(Open_Circuit) * V_(Induced) where:V_(Induced) = I_(Tx_Coil)ω M${A_{Open\_ Circuit}} = \frac{X_{2}}{\sqrt{R_{L\; 1}^{2} + X_{L\; 1}^{2} + X_{2}^{2} + {2X_{L\; 1}X_{2}}}}$where resistance of inductor L₁ is R_(L1)=X_(1A)/Q_(L1), reactance ofcapacitor C₂ is |X₂|=1/(ωC₂) and reactance of inductor L₁ is X_(L1)=ωL₁.Note that the open circuit voltage is only dependent on C₂ (not C₃), theequations above can be rearranged to accurately determine C₂. In analternative embodiment, when assuming that the Q_(L1) is relatively high(i.e. low R_(L1)), the following approximations can be made:

$X_{2} \cong \frac{X_{L1}}{{A_{Open\_ Circuit}} - 1}$ or$C_{2} \cong {\frac{{A_{Open\_ Circuit}} - 1}{\omega{A_{Open\_ Circuit}}X_{L1}}.}$

Once the open-circuit characteristics (and hence reactancecharacteristics of X₂), the loading conditions and power delivery can beused to calculate the magnitude of the Thevenin impedance and hence theremaining reactance variable of X₃. The equations relating Z_(TH) areshown above. Additionally when solving for the Thevenin equivalents withrespect to power, the following relationship can be used:

${V_{ac}}^{2} = {\frac{{V_{TH}}^{2}}{2} - {{P_{LOAD}R_{TH}} \pm \sqrt{\left( {\frac{{V_{TH}}^{2}}{2} - {P_{LOAD}R_{TH}}} \right)^{2} - {P_{LOAD}^{2}{Z_{TH}}^{2}}}}}$where the addition is used when R_(LOAD)>|Z_(TH)| (typical), thesubtraction is used when R_(LOAD)<|Z_(TH)|, and the Thevenin voltage isgiven by:

$V_{TH} = {V_{Induced}{\frac{{- j}{X_{2}}}{R_{L\; 1} + {j\left( {{X_{L\; 1}} - {X_{2}}} \right)}}.}}$

In some embodiments, the adjustment signal may be input to the tunablecapacitors themselves or a means for adjusting the value of a tunablecapacitor. For example, the adjustment signal may be input to a PWMgenerator, which would adjust the value of any of the tunable capacitorsdescribed herein, such as tunable capacitor C₁, C₂, or C₃ (see FIGS. 8A,8C, 8E, and 8G). In another example, the adjustment signal may be inputto a switch controller to switch to the appropriate value of a bank ofcapacitors. In yet another example, the capacitors may be tuned viaadjustment signals for mechanical or piezoelectric means. In a furtherexample, the adjustment signal for a BST capacitor can be provided as aDC voltage since the capacitance value of BST capacitor is a monotonicfunction of DC voltage bias.

Tuning Loop #5: Tune Matching According to a Function

In an exemplary embodiment, the tuning of the receiver matching can beadjusted based on a function determined by a processor of thecontroller, receiver, or both. FIG. 14A is a flowchart of an exemplarymethod for tuning based on a function. In step 1402, for a first set ofcapacitance values C_(2_value1), C_(3_value1) of capacitor positions C₂and C₃, respectively, rectified voltage V_(rect) and current I_(rect)can be measured and input to the processor. In step 1404, thesemeasurements can be repeated for a second set of capacitance valuesC_(2_value2), C_(3_value2) and input to the processor. In step 1406,having measurements for at least two or more sets of capacitance values,the processor may then fit a function for voltage V_(AC) induced oninductor L₁, load resistance R_(load), and/or change in inductance ΔL.In some embodiments, instead of using a “fit” to determine the function,an estimation of the function parameters (ΔL, V_(AC), and R_(load)) canbe sufficient to determine the desired values C_(2_desired),C_(3_desired). In some embodiments, a Gaussian Process can be used toquickly converge on the values of ΔL, V_(AC), and R_(load). In step1410, the processor can determine the next set of capacitance valuesC_(2_desired), C_(3_desired) for the desired voltage V_(AC). In someembodiments, the next set of capacitance values C_(2_desired),C_(3_value_desired) can be for the target or desired voltage V_(AC). Inan optional step, from the function, the processor can calculate theideal matching values for C₂ and C₃. In other embodiments, the next setof capacitance values C_(2_desired), C_(3_desired) can be at some pointbetween the sampled points (C_(2_value_1), C_(3_value_1), C_(2_value_2),C_(3_value_2)) and the ideal matching values of C₂ and C₃. In step 1412,the tunable capacitors in positions C₂ and C₃ can be adjusted accordingto C_(2_desired), C_(3_desired) via an adjustment signal from thecontroller. Note that the fit of the function can be repeated for eachnew set of measurements. FIG. 14B is an exemplary function of voltageV_(AC) as a function of capacitance C₂ and C₃ of a load resistanceR_(load) of 20Ω. Arrow 1414 shows the increasing direction of the scalefor voltage V_(AC), arrow 1416 shows how the function can change for achange in load resistance R_(load), and arrow 1418 shows the functioncan change for a change in inductance ΔL.

While the disclosed techniques have been described in connection withcertain preferred embodiments, other embodiments will be understood byone of ordinary skill in the art and are intended to fall within thescope of this disclosure. For example, designs, methods, configurationsof components, etc. related to transmitting wireless power have beendescribed above along with various specific applications and examplesthereof. Those skilled in the art will appreciate where the designs,components, configurations or components described herein can be used incombination, or interchangeably, and that the above description does notlimit such interchangeability or combination of components to only thatwhich is described herein.

All documents referenced herein are hereby incorporated by reference.

What is claimed is:
 1. A control system for a wireless power receiver,the control system comprising: a processing circuit configured toreceive two sensor signals, each sensor signal representative of acurrent or a voltage in the wireless power receiver, wherein, for eachsensor signal, the processing circuit comprises: a peak detectorconfigured to determine an amplitude of the sensor signal; a first mixerconfigured to produce a first mixed signal based on the sensor signal;and a second mixer configured to produce a second mixed signal based onthe sensor signal; and a controller coupled to the processing circuitand configured to determine a phase of the current or the voltage basedon the first mixed signals and the second mixed signals of the twosensor signals.
 2. The control system of claim 1, wherein each sensorsignal is received from a voltage sensor or a current sensor.
 3. Thecontrol system of claim 1, wherein at least one sensor signal comprisesfirst and second differential sensor signals.
 4. The control system ofclaim 3, wherein the processing circuit further comprises: an integratorconfigured to determine an integrated signal based on the differentialsensor signals, the integrator configured to provide the integratedsensor signal to the peak detector.
 5. The control system of claim 1,wherein the first mixer is configured to multiply the sensor signal witha first sinusoidal reference signal, and wherein the second mixer isconfigured to multiply the sensor signal with a second sinusoidalreference signal.
 6. The control system of claim 1, further comprising:a first low pass filter coupled to the first mixer and configured tofilter out second and higher order harmonics from the first mixedsignal; and a second low pass filter coupled to the second mixer andconfigured to filter out second and higher order harmonics from thesecond mixed signal.
 7. The control system of claim 1, whereincontroller is configured to determine an impedance signal based on afirst ratio and a second ratio, wherein: (i) the first ratio is of thefirst mixed signal of the first signal to the second mixed signal of thesecond signal, and (ii) the second ratio is of the first mixed signal ofthe second signal to the second mixed signal of the second signal. 8.The control system of claim 1, wherein the controller is configured todetermine a control system based on at least one of the determinedamplitude or determined phase.
 9. The control system of claim 8, whereinthe control signal is configured to control a switch of: (i) a tunablecapacitor of the receiver; (ii) an active rectifier of the receiver; or(iii) a safety mechanism of the receiver.
 10. The control system ofclaim 1, wherein the controller is implemented on anapplication-specific integrated circuit (ASIC).
 11. A wireless powerreceiver comprising: a circuit comprising a receiver inductor coupled inseries with at least one series capacitor; at least one parallelcapacitor coupled in parallel to the circuit; a rectifier coupled to theparallel capacitor; two sensors, each sensor coupled to the circuit, theparallel capacitor, or the rectifier, each sensor configured to generatea sensor signal representative of a current or a voltage signal; and acontrol system coupled to the two sensors and comprising: a processingcircuit configured to receive the two sensor signals, wherein, for eachsensor signal, the processing circuit comprises: a peak detectorconfigured to determine an amplitude of the sensor signal; a first mixerconfigured to produce a first mixed signal based on the sensor signal;and a second mixer configured to produce a second mixed signal based onthe sensor signal; and a controller coupled to the processing circuitand configured to determine a phase of the current or the voltage basedon the first mixed signals and the second mixed signals of the twosensor signals.
 12. The receiver of claim 11, wherein at least one ofthe two sensors is a voltage sensor configured to determine a voltageacross the circuit.
 13. The receiver of claim 11, wherein at least oneof the two sensors is a current sensor configured to determine a currentbetween the circuit and the rectifier.
 14. The receiver of claim 13,wherein the current sensor is configured to determine the currentbetween the circuit and the parallel capacitor.
 15. The receiver ofclaim 14, further comprising: at least one additional capacitor coupledbetween the parallel capacitor and the rectifier, wherein the currentsensor is configured to determine the current between the parallelcapacitor and the additional capacitor.
 16. The receiver of claim 15,wherein the additional capacitor is tunable based on the control signal.17. The receiver of claim 11, wherein at least one of the seriescapacitor or the parallel capacitor is tunable based on the controlsignal.
 18. The receiver of claim 11, wherein the rectifier is an activerectifier and is configured to be controlled based on the controlsignal.
 19. The receiver of claim 11, wherein the controller isconfigured to produce a control signal based on the determined amplitudeand determined phase, the control signal configured to control a switchof: (i) a tunable capacitor of the receiver; (ii) an active rectifier ofthe receiver; or (iii) a safety mechanism of the receiver.
 20. A controlmethod for a wireless power receiver, the receiver comprising (a) areceiver inductor coupled in series with at least one series capacitorand (b) a rectifier, the method comprising: receiving, by a controlsystem, two sensor signals, each sensor signal representative of acurrent or a voltage in the receiver; for each sensor signal:determining, by a peak detector of the control system, an amplitude ofthe sensor signal; producing, by a first mixer of the control system, afirst mixed signal based on the sensor signal; and producing, by asecond mixer of the control system, a second mixed signal based on thesensor signal; determining the phase of the sensor signal based on thefirst mixed signals and the second mixed signals of the two sensorsignals; and providing a control signal based on the determinedamplitude and determined phase to at least one of: (i) a tunablecapacitor of the receiver, (ii) an active rectifier of the receiver, or(iii) a safety mechanism of the receiver.